Characterizing geotechnical anisotropic spatial variations using random field theory

In this study, anisotropic heterogeneous geotechnical fields are characterized using random field theory, in which five basic patterns of material anisotropy are simulated including isotropy, transverse anisotropy, rotated anisotropy, general anisotropy, and general rotated anisotropy. Theoretical formulations of scale of fluctuation as a function of directional angle are developed for the five basic patterns of anisotropy through modifications of the coordinate system. These formulations of scale of fluctuation are identical for different correlation structures. Correlation functions for the exponential and Gaussian correlation structures are also derived. The matrix decomposition method is then applied to generate anisotropic random fields. The generated random field correlated data are verified with two realizations of transverse anisotropy and general rotated anisotropy random fields. Test values of the sample mean, sample deviation, and scales of fluctuation in six directions match well with the prescribed values. This study provides a technique to characterize inherent geotechnical variability and anisotropy, which is required to realistically simulate complex geological properties in engineering reliability analysis and design.